The legendary London Underground roundel. Photograph: Frank Baron for the Guardian

I asked a bunch of people close to the Tube strike negotiations the same thing over the weekend. Would the RMT union have called the latest stoppages if Bob Crow were still alive? They all answered with a straight "no". Some of those I approached were unlikely to have said anything else. Even so, the sudden death last month of the much-monstered late RMT leader forms a big part of the context in which the first of the latest Tube strikes are going ahead and will be interpreted by parties to the dispute.

Crow's passing brought some belated recognition that the so-called thug and bully who led the RMT was respected by his members and London Underground management alike as a man who knew when it was time to make a deal. Although depicted by outsiders as an obdurate hardliner, he was seen by senior Tube managers as a realist and, in RMT terms, a moderate pragmatist – a "statesman", no less, in the word of one London transport chief - who always grasped when it was wise to make a compromise or tactical withdrawal.

Tube bosses say it was that wisdom which resulted in the second of two strikes over ticket office closures and job reductions and restructuring in February being called off. They argue that Crow recognised that support among RMT members was falling, which would have enabled over 50% of the Underground service to have run, leaving the union looking weak. The same judgement, they claim, would have meant that the latest strikes would not have been called at all. My strong impression is that the TSSA union, whose members took part in the strike in February that went ahead but aren't taking part in this one, agree. There's been a bit of a falling out.

The RMT's case is that London Underground's management has wrecked talks seeking a resolution by breaching trust. However, part of the backdrop is the contest to succeed Crow as the RMT's general secretary, which the union's critics say has left a leadership vacuum in which contenders for the top job are positioning themselves in the eyes of their members as the toughest negotiator and therefore best potential next general secretary of one of the most successful unions in the country. According to this view, even if some in leadership positions wanted to avert the latest strikes, none wants to risk being depicted as a quitter, splitter or compromiser in the eyes of the RMT electorate.

Some interested observers have always maintained that management too sees at least some longer-term advantage from the latest strikes going ahead should they show the union to be less powerful than it and some of its members had hoped or previously thought (not to mention Boris Johnson, who chairs Transport for London's board, who wouldn't mind being seen as the mayor who presided over the taming of the RMT). Management says it already has the 750 voluntary redundancies it wants. Certainly, the impact of the strike is bound be less than it would otherwise have been thanks to the non-participation this time round of TSSA members.

The RMT, though, remains defiant. Its picket lines are organised, its rhetoric is strident and it will believe there's still plenty to fight for both now and in the future. The next few days might reveal a little more about the web of power struggles within the larger London Underground dispute.